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Math Help - An equation

  1. #1
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    An simple algebraic equation (x^2)

    Hello everyone, I have got a quite nice equation to solve. I have worked some on it but it don't go pretty well.

    The equation is:

    \frac { 1 - 3x^2 } { 4 - x^2 } = \frac { 9x - 1 } { 3x - 6 }

    My thoughts on how to solve it.

    1 Get rid of the denominators

    Multiply with both numerators.

    2 Open up the parenthesises and put everything either left/right of '='.

    That would result in 17x^2 - 23x = 0

    Going from here isn't too hard, but the anser I get is quite different from the books answer.

    Thanks for all replies.
    Last edited by λιεҗąиđŗ; September 27th 2007 at 05:28 AM. Reason: Title edit
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by λιεҗąиđŗ View Post
    \frac { 1 - 3x^2 } { 4 - x^2 } = \frac { 9x - 1 } { 3x - 6 }

    My thoughts on how to solve it.

    1 Get rid of the denominators

    Multiply with both numerators.

    2 Open up the parenthesises and put everything either left/right of '='.

    That would result in 17x^2 - 23x = 0

    Going from here isn't too hard, but the anser I get is quite different from the books answer.

    Thanks for all replies.
    Your method of attack sounds good.

    So:
    \frac { 1 - 3x^2 } { 4 - x^2 } = \frac { 9x - 1 } { 3x - 6 }

    Let's multiply both sides by (4 - x^2)(3x - 6):
    \frac { 1 - 3x^2 } { 4 - x^2 } \cdot (4 - x^2)(3x - 6) = \frac { 9x - 1 } { 3x - 6 } \cdot (4 - x^2)(3x - 6)

    (1 - 3x^2 )(3x - 6) = (9x - 1)(4 - x^2)

    Let's take a moment here and do some factoring:
    3x - 6 = 3(x - 2)
    4 - x^2 = (2 + x)(2 - x) = -(x + 2)(x - 2)

    Thus
    3(1 - 3x^2 )(x - 2) = -(9x - 1)(x + 2)(x - 2)

    Cancel the common x - 2:
    3(1 - 3x^2) = -(9x - 1)(x + 2)

    Now expand:
    3 - 9x^2 = -(9x^2 + 18x - x - 2);~x \neq -2

    3 - 9x^2 = -9x^2 - 17x + 2;~x \neq -2

    3 = -17x + 2;~x \neq -2

    17x = -1;~x \neq -2

    x = -\frac{1}{17};~x \neq -2

    Since x \neq 2 anyway, we can drop this part. Thus
    x = -\frac{1}{17}

    -Dan
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